Abstract : PSR J1906+0746 is a young pulsar in the relativistic binary with the second-shortest known orbital period, of 3.98 hours. We here present a timing study based on five years of observations, conducted with the 5 largest radio telescopes in the world, aimed at determining the companion nature. Through the measurement of three post-Keplerian orbital parameters we find the pulsar mass to be 1.29111 M sol, and the companion mass 1.32211 M sol respectively. These masses fit well in the observed collection of double neutron stars, but are also compatible with other white dwarfs around young pulsars such as J1906+0746. Neither radio pulsations nor dispersion-inducing outflows that could have further established the companion nature were detected. We derive an HI-absorption distance, which indicates that an optical confirmation of a white dwarf companion is very challenging. The pulsar is fading fast due to geodetic precession, limiting future timing improvements. We conclude that young pulsar J1906+0746 is likely part of a double neutron star, or is otherwise orbited by an older white dwarf, in an exotic system formed through two stages of mass transfer.